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Abstract Let $$T$$ be a satellite knot, link, or spatial graph in a 3-manifold $$M$$ that is either $S^3$ or a lens space. Let $$\b_0$$ and $$\b_1$$ denote genus 0 and genus 1 bridge number, respectively. Suppose that $$T$$ has a companion knot $$K$$ (necessarily not the unknot) and wrapping number $$\omega$$ with respect to $$K$$. When $$K$$ is not a torus knot, we show that $$\b_1(T)\geq \omega \b_1(K)$$. There are previously known counter-examples if $$K$$ is a torus knot. Along the way, we generalize and give a new proof of Schubert's result that $$\b_0(T) \geq \omega \b_0(K)$$. We also prove versions of the theorem applicable to when $$T$$ is a "lensed satellite" and when there is a torus separating components of $$T$$. 

Effective file system testing relies on coverage to detect bugs and enhance reliability. We analyzed real file system bugs and found a weak correlation between code coverage, the most commonly used metric, and test effectiveness; many bugs were in covered code but remained undetected. Our study also showed that covering diverse file system inputs and outputs—system call arguments and return values—can be key to detecting the majority of observed bugs. We present input coverage and output coverage as new metrics for evaluating and improving file system testing, and have developed the IOCov framework for computing these metrics. Unlike existing system call tracers, IOCov computes coverage using only the calls relevant to testing, excluding unrelated ones that should not be counted. To demonstrate IOCov’s utility, we used it to extend the existing testing tool CrashMonkey into CM-IOCov, which achieves broader input coverage and more thorough detection of crash consistency bugs. Our experimental evaluation shows that IOCov com- putes input and output coverage accurately with minimal overhead. IOCov is applicable to different types of file system testing and can provide insights for improvement as well as identify untested cases based on coverage results. Moreover, the bugs found exclusively by CM-IOCov are 2.1 and 12.9 times more than those found exclusively by CrashMonkey on the 6.12 and 5.6 kernels, respectively, demonstrating the effectiveness of the IOCov-based coverage approach. 

Animal tissues exist within a continuum of fluid to solid states, and transitions between states are important for embryonic development, wound healing and cancer metastasis. Fluid-to-solid transitions are governed by the ratio of adhesive energy to kinetic energy. Here, we find that presomitic mesoderm solidification is driven by an intrinsic decline in cell speed along with an increase in adhesion mediated by Cadherin 2 in parallel with fibronectin and its receptor Integrin α5. A computational model of cell–cell adhesion in the central tissue mesenchyme and cell–ECM adhesion on the tissue surface explains the observed phenotypes. Further, we identify negative feedback within the ECM as fibronectin supports the formation of a separate layer of Fibrillin 2b matrix that inhibits solidification. These data reveal a tissue fluidity code in which solidification is promoted by cadherins in parallel with Integrin α5 and fibronectin, whereas negative feedback through Fibrillin 2b promotes fluidization. 

Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of interest. However, there is a dearth of data-driven methods for identifying frequency bands that optimally summarize frequency-domain information in the time series. A new method to identify partition points in the frequency space of a multivariate locally stationary time series is proposed. These partition points signify changes across frequencies in the time-varying behavior of the signal and provide frequency band summary measures that best preserve nonstationary dynamics of the observed series. An $$L_2$$-norm based discrepancy measure that finds differences in the time-varying spectral density matrix is constructed, and its asymptotic properties are derived. New nonparametric bootstrap tests are also provided to identify significant frequency partition points and to identify components and cross-components of the spectral matrix exhibiting changes over frequencies. Finite-sample performance of the proposed method is illustrated via simulations. The proposed method is used to develop optimal frequency band summary measures for characterizing time-varying behavior in resting-state electroencephalography time series, as well as identifying components and cross-components associated with each frequency partition point. 

Abstract South American summer monsoon (SASM) strength tracks insolation on orbital timescales, linking global climate and continental hydrology. However, whether local water availability also responds to global climate forcings is unclear. Here, we present water balance records from Lake Junín, an Andean lake within the SASM domain. Local water balance and SASM strength is inferred from triple oxygen isotopes of lake carbonates during two interglacial periods (Marine Isotope Stage (MIS) 15, 621–563 ka; the Holocene, 11.7–0 ka). We find SASM strength and water balance both follow the precession‐pacing of local summer insolation, with the driest conditions occurring at Lake Junín under weakened SASM conditions (and vice versa). Further, the largest variations occurred during MIS 15, when insolation was more variable than the Holocene. These results suggest that global climate influences South American hydrology on both the local and continental scales, with implications for tropical water resources, the atmospheric greenhouse effect, and ecosystem dynamics. 

Prior studies of halobenzene−ammonia complexes have shown that the nature of the cationic intermediate (i.e., Wheland-type vs ion-radical) may play a key role in determining the reaction products. To probe this link, we report here the reaction dynamics of the chlorobenzene-ammonia 1:1 complex (PhCl···NH3) using product ion imaging following two-color resonant two-photon ionization. A threshold value of 8.863 ± 0.008 eV was determined for the appearance of protonated aniline, which accompanies Cl atom loss and is the dominant product channel at energies near threshold. Scanning down to energies close to threshold, we find no evidence for a roaming halogen radical mechanism leading to HCl products, which was evidenced in the related bromobenzene−ammonia complex, and proceeded through an ion-radical intermediate structure. Here, supporting calculations indicate that both types of intermediates are present, but the Wheland-type structure is significantly more stable. Addressing a key question of earlier work, analysis of the PhCl···NH3 potential energy surface (PES) in the reactant region establishes a complicated entrance channel pathway linking the in-plane σ-type complex to the Wheland intermediate (iWH) on the [PhCl···NH3]+• cationic surface. This pathway involves stepwise transition of the weakly bound ammonia from the initial in-plane σ-type complex to an ortho Wheland intermediate, followed by rearrangement to the ipso position. Finally, given that fluorine has been shown to stabilize aromatic ions, we hypothesized that fluorine substitution might alter the structure of the intermediate, favoring the ion-radical intermediate. To test this hypothesis, as an illustrative example the PES of the meta-PhClF-NH3 system on the cationic surface was computed. Confirming our hypothesis, these calculations show an inversion in stability for the Wheland-type and ion−radical complex intermediates, with the latter preferred energetically at the examined level of theory. 

Although rates of fluvial incision across the Colorado Plateau are known reasonably well, rate variability through time and its controlling processes are still poorly understood. We used boulder armored benches from the Teasdale-Torrey lowlands reach of the Fremont River in the northwestern Colorado Plateau (Utah, USA) as temporal markers to determine regional incision rates and explore controls on rate variability. Bench gravels are sourced from Tertiary volcanic rocks capping nearby Boulder and Thousand Lakes Mountains. The sedimentology of bench deposits suggests that most form from mass movement with later fluvial reworking. Volcanic boulders are tougher than the local sedimentary bedrock, which promotes boulder armoring and topographic inversion. Thirty-seven boulder cosmogenic 3He exposure ages from 11 different benches range from >600 ka to ca. 100 ka. Soil carbonate stages from two benches are in good agreement with surface exposure ages. Averaged Fremont River and tributary incision rates determined from bench exposure ages are 32% faster for tributaries off of Thousand Lakes Mountain (0.41 m/k.y.) than tributaries off of Boulder Mountain (0.28 m/k.y.). This difference in incision rate may be due to Laramideage structures limiting incision for the tributaries that drain Boulder Mountain and extensive Pleistocene ice caps on Boulder Mountain creating a wider and thicker boulder armor slowing incision. 

Abstract Analysis of ion-kinetic instabilities in solar wind plasmas is crucial for understanding energetics and dynamics throughout the heliosphere, as evident from spacecraft observations of complex ion velocity distribution functions (VDFs) and ubiquitous ion-scale kinetic waves. In this work, we explore machine learning (ML) and deep learning (DL) classification models to identify unstable cases of ion VDFs driving kinetic waves. Using 34 hybrid particle-in-cell simulations of kinetic protons andα-particles initialized using plasma parameters derived from solar wind (SW) observations, we prepare a data set of nearly 1600 VDFs representing stable/unstable cases and associated plasma and wave properties. We compare feature-based classifiers applied to VDF moments, such as support vector machine and random forest (RF), with DL convolutional neural networks (CNNs) applied directly to VDFs as images in the gyrotropic velocity plane. The best-performing classifier, RF, has an accuracy of 0.96 ± 0.01, and a true skill score of 0.89 ± 0.03, with the majority of missed predictions made near stability thresholds. We study how the variations of the temporal derivative thresholds of anisotropies and magnetic energies, and sampling strategies for simulation runs, affect classification. CNN-based models have the highest accuracy of 0.88 ± 0.18 among all considered if evaluated on the runs entirely not used during the model training. The addition of theE_⊥power spectrum as an input for the ML models leads to the improvement of instability analysis for some cases. The results demonstrate the potential of ML and DL for the detection of ion-scale kinetic instabilities using spacecraft observations of SW and magnetospheric plasmas. 

We use thin position of Heegaard splittings to give a new proof of Haken's Lemma that a Heegaard surface of a reducible manifold is reducible and of Scharlemann's ``Strong Haken Theorem'': a Heegaard surface for a 3-manifold may be isotoped to intersect a given collection of essential spheres and discs in a single loop each. We also give a reformulation of Casson and Gordon's theorem on weakly reducible Heegaard splittings, showing that they exhibit additional structure with respect to certain incompressible surfaces. This article could also serve as an introduction to the theory of generalized Heegaard surfaces and it includes a careful study of their behaviour under amalgamation.